Prove that `sin^(-1)x+sin^(-1)sqrt(1-x^(2))=(pi)/(2)`

Prove that sin^(-1)x=cos^(-1) sqrt(1-x^2)

Prove that 2sin^(-1)x=sin^(-1)[2x sqrt(1-x^(2))]

sin^(-1)sqrt(x)+sin^(-1)sqrt(1-x)=(pi)/(2)

Prove that, 2 sin^(-1)x = sin^(-1) (2x sqrt (1-x^2))

If x<0, then prove that cos^(-1)x=pi-sin^(-1)sqrt(1-x^2)

Prove that: sin^(-1){(sqrt(1+x)+sqrt(1-x))/(2)}=(pi)/(4)+(sin^(-1)x)/(2),0

Prove that sin^(-1). ((x + sqrt(1 - x^(2)))/(sqrt2)) = sin^(-1) x + (pi)/(4) , where - (1)/(sqrt2) lt x lt(1)/(sqrt2)

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))

If x lt 0 , then prove that cos^(-1) x = pi - sin^(-1) sqrt(1 - x^(2))